Applied Iterative Methods

Charles L. Byrne (Autor)

Buch | Softcover

400 Seiten

2021
CRC Press (Verlag)
978-0-367-44616-1 (ISBN)

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This book is a collection of essays on iterative algorithms and their uses. It focuses on the mathematics of medical image reconstruction, with emphasis on Fourier inversion. The book discusses the problems and algorithms in the context of operators on finite-dimensional Euclidean space.

Applied Iterative Methods is a self-contained treatise suitable as both a reference and a graduate-level textbook in the area of iterative algorithms. It is the first book to combine subjects such as optimization, convex analysis, and approximation theory and organize them around a detailed and mathematically sound treatment of iterative algorithms. Such algorithms are used in solving problems in a diverse area of applications, most notably in medical imaging such as emission and transmission tomography and magnetic-resonance imaging, as well as in intensity-modulated radiation therapy. Other applications, which lie outside of medicine, are remote sensing and hyperspectral imaging. This book details a great number of different iterative algorithms that are universally applicable.

Byrne /, Charles L.

Part I: Preliminaries 1. Introduction 2. Background 3. BasicConcepts 4. Metric Spaces and Norms Part II: Overview 5. Operators 6. Problems and Algorithms Part III: Operators 7. Averaged and Paracontractive Operators Part IV: Algorithms 8. The Algebraic Reconstruction Technique 9. Simultaneous and Block-Iterative ART 10. Jacobi and Gauss-Seidel Methods 11. Conjugate-Direction Methods in Optimization Part V: Positivity in Linear Systems 12. The Multiplicative ART (MART) 13. Rescaled Block-Iterative (RBI) Methods Part VI: Stability 14. Sensitivity to Noise 15. Feedback in Block-Iterative Reconstruction Part VII: Optimization 16. Iterative Optimization 17. Convex Sets and Convex Functions 18. Generalized Projections onto Convex Sets 19. The Split Feasibility Problem 20. Nonsmooth Optimization 21. An Interior-Point Optimization Method 22. Linear and Convex Programming 23. Systems of Linear Inequalities 24. Constrained Iteration Methods 25. Fourier Transform Estimation Part VIII: Applications 26. Tomography 27. Intensity-Modulated Radiation Therapy 28. Magnetic-Resonance Imaging 29. Hyperspectral Imaging 30. Planewave Propagation 31. Inverse Problems and the Laplace Transform 32. Detection and Classification

Erscheinungsdatum	10.05.2021
Verlagsort	London
Sprache	englisch
Maße	152 x 229 mm
Gewicht	453 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Technik ► Umwelttechnik / Biotechnologie
ISBN-10	0-367-44616-2 / 0367446162
ISBN-13	978-0-367-44616-1 / 9780367446161
Zustand	Neuware